Benjo please correct me if I am wrong
You are working for a national scaffolding company,with several area branches up and down the UK. The work in your area has dried up and you are now working on a job that was tendered for by another branch.
One reason your branch is dragging it's feet on paying travel,could be that the job you are working on is not "theirs" but is on the books of the "Sheffield branch" being local to them they would have put less into the tender for travel and expenses.
however you are entitled to payments for your travel time,You could always ring the HR department at head office and put your grievance to them.
Branch managers make all sorts of deals between themselves for a variety of reasons, one of which will be to find work for their lads when work in their area is slack.Head office will not necessary be aware of these deals.